''There is no deep, serious lack of understanding,'' Mr. Shultz said at a press conference after his meetings. ''But there are a number of complicated issues in which the positions of the US and France are not identical.''

France remains ''a good and solid ally,'' added Michel Vauzelle, President Francois Mitterrand's spokesman. He warned, though, that America must ''respect her sovereignty'' and not treat France as a ''vassal.''

Mr. Vauzelle was referring to the American attempt to reach an agreement with the allies restricting trade with the Soviets. The basis of an agreement was announced last month by President Reagan when he lifted American sanctions on exports for the Siberian gas pipeline.

The French, though, immediately said they were not party to any such accord. Although Mr. Shultz said he was confident that the ''right framework'' would be found to bring the French around, he did not seem to budge Mr. Mitterrand.

''France does not want an economic NATO, and no country, even a friend, can dictate her conduct,'' Mr. Vauzelle said. ''Mr. Shultz left convinced of our firmness on this point.''

Mr. Shultz said there were indeed philosophical differences between Paris and Washington over trade with the Soviets. But he suggested that the French are willing to restrict trade to a certain extent, and that their main objection at this point was over ending subsidized credits. The French insist they need government-supported credits to compete effectively with the other allies' exports to the Soviet Union.

As much as Mr. Shultz talked with the French about economic issues, he also talked about military issues. Here, too, for the first time since Mr. Mitterrand took power, the two countries seem to be in disagreement on strategy.

Recently, Mr. Mitterrand has been saying that the American zero-zero option, calling for the Soviets to withdraw all its East European-based SS-20 missiles in return for the US forgoing deployment of 572 crusie and Pershing missiles in Western Europe, might be unrealistic.

Mr. Mitterrand continues to stress that the planned deployment of American Pershing II missiles in Europe next year is justified to counter the Soviet missiles already in place. But he now adds, as he told American columnist Joseph Kraft this week, that ''the solution could be somewhere between the freeze of the present situation that the Soviets are advancing and the zero option advocated by the American.''

In other words, the Soviets would withdraw some of their missiles in return for an American agreement to not deploy its missiles.

While Mr. Mitterrand's statements seemed to represent his first break with the official NATO position endorsing the zero option as the best negotiating stance, American officials here are not fuming.

''It's not the unravelling of the alliance stand,'' an American diplomat said. But the same diplomat added that combined with recent decision by the Mitterrand government to cut French conventional forces, there was indeed American worry that the French were toning down their support of the alliance.

Under budget pressure, Mr. Mitterrand is planning to reduce the French Army's strength over five years. The Air Force is to lose 7,000 men and the Navy 5,000. Plans for the nuclear force de frappe, though, are not being squeeze by one centime.

At the same time, the Reagan administration is stressing the need for modernizing conventional forces in Western Europe. This thinking worries the French, who argue that it will fan neutralism in Europe. Top French officials are unanimous in saying in private that a neutral West Germany is their No. 1 fear.

The Americans are upset about the French military cutbacks for the same reason: They fear this might erode allied support for larger military budgets. In addition, the Americans believe, as a diplomat put it, that ''the force de frappe is not very impressive.''

This remark hints at what the American believes the fundamental problem is between Paris and Washington. Mr. Mitterrand, continuing in good Gaullist tradition, insists that the French must act independently of the US. But deep down the Americans feel that the French are dependent on the American nuclear umbrella and thus don't have the power to truly assert independence.

So when Mr. Mitterrand made conciliatory moves after he took office, the American diplomat said, ''We were lulled into believing relations could be smooth.'' Today, though, after months of snapping over economic strategy, the American added that the new military divergence between the two countries, ''doesn't make us that much more irritated.''

Franco-American relations, he repeated, are just back to their normal mess.